If α=−4+5i is the root of the quadratic equation f(x)=0, then β=−4−5i is also the root of the quadratic equation f(x)=0.
α=−4+5i,β=−4−5i
Hence
f(x)=a(x−α)(x−β),a=0
f(x)=a(x−(−4+5i))(x−(−4−5i))
α+β=−4+5i−4−5i=−8=−ab
α⋅β=(−4+5i)⋅(−4−5i)=(−4)2+(5)2=41=ac
f(x)=ax2+8ax+41a,a=0
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